Concrete activities and experiences are emphasised and outlined throughout the pupil books. The Teachers Resource Book (TRB) also provides further suggestion for the ways in which a teacher can use concrete activities with their class.
These experiences are then further developed via the pictorial activities; this may be through interaction with the digital resources and/or via the write-in activities in the books. Of the CPA approach, exploring pictorial representations of materials, numbers, shapes etc., is a vital (but sometimes neglected, particularly at the senior end) step on a child’s journey towards understanding.
All of this should greatly enhance the children’s ability to visualise and understand maths and be more prepared when they meet the more traditional, abstract activities.

Active participation

The high number of concrete based activities within Operation Maths ensures that the children have regular, if not daily, opportunities to be engaged in active learning. The inclusion of free mini-whiteboards (MWBs) as part of the programme also encourages the active involvement of all the class in any activities as all children must visibly participate. Moreover, the custom-made suite of write-hide-show videos and Maths around us videos (see below for samples) further increase the opportunities to use the MWBs. I challenge you to show the estimation video to your class and not have them all excited and active!

Mastery curriculum

Research suggests that changing chapters/topics every week, especially in senior end and especially the case of number topics, is not conducive to developing a strong understanding for the various topics and that preferable to this is a mastery curriculum approach, where the children are afforded a longer time to engage with, and ultimately master, the concepts. Therefore, in Operation Maths, these topics have a dedicated two weeks block, allowing the children to fully engage with the concepts before moving to a different topic, thereby increasing the likelihood for the children to master the content. So, if you look at the contents page of the Operation Maths books, you will notice that there are fewer chapters than usual but that many of these are “double” chapters, designed to be taught over ten school days, as opposed to five.

A better understanding of the operations

Similarly, research suggests that teaching opposite or inverse operations together, allows the children to better grasp the connections between the two, therefore promoting deeper conceptual understanding. So, in the senior end, addition and subtraction are taught together as part of the same chapter(s), as are multiplication and division. A similar approach is taken to the operations in first and second class once the children have been formally introduced to subtraction.

A seamless transition…

I was primarily involved in authoring all of the number and algebra chapters in the 3rd to 6th class books, while my co-authors Michael Browne and Siobhán Kelleher authored the chapters for measures, data, shape and space for the same classes. This means that, for the children, their experience of the content is very cohesive as it flows seamlessly from one class to the next.
Similarly the 5th and 6th class books were written in light of the NCCA Bridging documents and Project Maths at junior cycle in second level. In particular, extra attention was paid to the correct and accurate use of mathematical terminology which also helps ensure that the child’s transition from primary maths to second level maths is also as seamless as possible.

Other ways in which Operation Maths promotes the development of deeper connections and understanding include:

Linkage: the topics are all taught in a very connected way, with cross references being made where appropriate. In particular, measures are not just confined to their own chapters: they are taught in an integrated way across all suitable chapters and particularly across number

Integration: The use of maths across other subjects is also emphasised regularly and particularly as part of the suggested activities in the TRBs. In the senior end there are also themed revision pages in the Pupil’s Book, where maths is explored through History, Geography, Sports etc.

The books have a clean, uncluttered design making them easier for children to focus on the concepts and not be distracted by unnecessary images

In the senior end, the Pupil’s Book also has clear and detailed teaching panels (easily identifiable by their yellow background) right throughout each chapter, to aid both the teachers and the children, and can be particularly useful if the children are working independently or in small groups.

To help make connections with the environment there are dedicated Maths Around Us videos in the digital resources, Maths Around Us activities in the Pupil’s Book and Maths Trails in the TRB photocopiables and in selected Discovery Books

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